| In recent years, we have witnessed a widespread use of first-order methods (FOMs) to solve large-scale structured convex optimization problems. One fundamental issue concerning FOMs is their convergence properties. In this talk, we will present a framework for analyzing the convergence rates of FOMs. A key component of this framework is a so-called error bound condition, which provides a tractable bound on the distance from any candidate solution to the optimal solution set of the problem at hand. We will show that many structured convex optimization problems that arise in practice satisfy the error bound condition. Consequently, we are able to show that many FOMs have a linear rate of convergence when applied to those problems. | |